Trying to create visualization of EM waves
You can recreate the first image fairly well using the math function mesh (Add --> Mesh --> Math Function --> Z Math Function).

This is what we're aiming for here:


First, you need to enable the AddMesh:Extra Objects add-on (press CtrlAltU to access the system preferences)



Type in the wave function you want to display in the input box (I used Z = sin(x) + sin(y) for this example).



Then, delete the edges along one axis (I deleted the ones along X):


Select and add each edge loop using AltShiftRight Mouse Button.
After you've got 'em all, delete edges and faces only (X --> Only Edges and Faces).




From here you can take it to many different places, but here's a suggested workflow:


Convert the mesh to a curve, then add a fill.





Add a taper object (bezier curve with an arch shape along the Y axis), and set it as a taper object for the wave curve.





Add a subsurf modifier to get smoother curves.

In Cycles, set an emission material to the wave object and choose a proper color.





If you want to add particles for added effect, create another copy of the original wave mesh, then add a particle system to it.





Add a simple mesh circle (Add --> Mesh --> Circle).

Set Fill type: Triangle Fan

and Vertices: 6


Then rotate 90 degrees on X so that the circle faces the Y axis.

Apply rotation (CtrlA --> Rotation).

Apply the same material you created for the wave to this circle.


Use the following particle settings:

Emission:
Number: 50000
Jittering Amount: 2

Velocity:
Random: 2
Rot: 1

Physics:
Size: 0.025
Random Size: 1
Mass: 0

Render:
Emitter: False (uncheck)
Render type: Object
Dupli Object: The hexagonal circle you created earlier.
In the Scene tab on the Properties Window, turn Gravity off.





Run the animation (AltA) for a bit until you have a nice distribution of particles around your mesh.


That's about it!

You can enhance this further by adding depth of field or motion blur, but I'll let you find tutorials or other answers to find out how to do this.